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ellip.m

## Copyright (C) 2001 Paulo Neis
##
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2 of the License, or
## (at your option) any later version.
##
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program; If not, see <http://www.gnu.org/licenses/>.
## 

## N-ellip 0.2.1
##usage: [Zz, Zp, Zg] = ellip(n, Rp, Rs, Wp, stype,'s')
##
## Generate an Elliptic or Cauer filter (discrete and contnuious).
## 
## [b,a] = ellip(n, Rp, Rs, Wp)
##  low pass filter with order n, cutoff pi*Wp radians, Rp decibels 
##  of ripple in the passband and a stopband Rs decibels down.
##
## [b,a] = ellip(n, Rp, Rs, Wp, 'high')
##  high pass filter with cutoff pi*Wp...
##
## [b,a] = ellip(n, Rp, Rs, [Wl, Wh])
##  band pass filter with band pass edges pi*Wl and pi*Wh ...
##
## [b,a] = ellip(n, Rp, Rs, [Wl, Wh], 'stop')
##  band reject filter with edges pi*Wl and pi*Wh, ...
##
## [z,p,g] = ellip(...)
##  return filter as zero-pole-gain.
##
## [...] = ellip(...,'s')
##     return a Laplace space filter, W can be larger than 1.
## 
## [a,b,c,d] = ellip(...)
##  return  state-space matrices 
##
## References: 
##
## - Oppenheim, Alan V., Discrete Time Signal Processing, Hardcover, 1999.
## - Parente Ribeiro, E., Notas de aula da disciplina TE498 -  Processamento 
##   Digital de Sinais, UFPR, 2001/2002.
## - Kienzle, Paul, functions from Octave-Forge, 1999 (http://octave.sf.net).
##
## Author: Paulo Neis <p_neis@yahoo.com.br>
## Modified: Doug Stewart Feb. 2003


function [a,b,c,d] = ellip(n, Rp, Rs, W, varargin)

  if (nargin>6 || nargin<4) || (nargout>4 || nargout<2)
    usage ("[b, a] or [z, p, g] or [a,b,c,d] = ellip (n, Rp, Rs, Wp, [, 'ftype'][,'s'])");
  endif

  ## interpret the input parameters
  if (!(length(n)==1 && n == round(n) && n > 0))
    error ("ellip: filter order n must be a positive integer");
  endif


  stop = 0;
  digital = 1;  
  for i=1:length(varargin)
    switch varargin{i}
    case 's', digital = 0;
    case 'z', digital = 1;
    case { 'high', 'stop' }, stop = 1;
    case { 'low',  'pass' }, stop = 0;
    otherwise,  error ("ellip: expected [high|stop] or [s|z]");
    endswitch
  endfor

  [r, c]=size(W);
  if (!(length(W)<=2 && (r==1 || c==1)))
    error ("ellip: frequency must be given as w0 or [w0, w1]");
  elseif (!(length(W)==1 || length(W) == 2))
    error ("ellip: only one filter band allowed");
  elseif (length(W)==2 && !(W(1) < W(2)))
    error ("ellip: first band edge must be smaller than second");
  endif

  if ( digital && !all(W >= 0 & W <= 1))
    error ("ellip: critical frequencies must be in (0 1)");
  elseif ( !digital && !all(W >= 0 ))
    error ("ellip: critical frequencies must be in (0 inf)");
  endif

  if (Rp < 0)
    error("ellip: passband ripple must be positive decibels");
  endif

  if (Rs < 0)
    error("ellip: stopband ripple must be positive decibels");
  end


  ##Prewarp the digital frequencies
  if digital
    T = 2;       # sampling frequency of 2 Hz
    W = tan(pi*W/T);
  endif

  ##Generate s-plane poles, zeros and gain
  [zero, pole, gain] = ncauer(Rp, Rs, n);

  ## splane frequency transform
  [zero, pole, gain] = sftrans(zero, pole, gain, W, stop);

  ## Use bilinear transform to convert poles to the z plane
  if digital
    [zero, pole, gain] = bilinear(zero, pole, gain, T);
  endif


  ## convert to the correct output form
  if nargout==2, 
    a = real(gain*poly(zero));
    b = real(poly(pole));
  elseif nargout==3,
    a = zero;
    b = pole;
    c = gain;
  else
    ## output ss results 
    [a, b, c, d] = zp2ss (zero, pole, gain);
  endif

endfunction


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